{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Copyright &copy; 2013 Ondrej Martinsky, All rights reserved\n",
    "\n",
    "[www.quantandfinancial.com](http://www.quantandfinancial.com)\n",
    "# Diversification benefit in mean-variance portfolio optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using matplotlib backend: Qt5Agg\n",
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab\n",
    "%matplotlib inline\n",
    "pylab.rcParams['figure.figsize'] = (10, 6)\n",
    "import scipy.optimize\n",
    "from pandas import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "r_a = 0.04\n",
    "r_b = 0.05\n",
    "stdev_a = 0.07\n",
    "stdev_b = 0.08"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6dVzXrKZ+u3bFZDLEpmBuaUazVo1rpQ4qg1Lq7hFCQ0OxtLRk0qRJBW4eHpoV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\nnJw8rZArNjfiIWB4UgSzpxrJTDWQGNk1LyXpRkrYmwPL/w6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MAAAg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\nRJIyfjUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x28f21333898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for correl in linspace(-1,1,5):\n",
    "    X, Y = [], []\n",
    "    for w_a in linspace(0,1,100):\n",
    "        w_b = 1 - w_a\n",
    "        r = r_a * w_a + r_b * w_b\n",
    "        var = w_a**2 * stdev_a**2 + w_b**2 * stdev_b**2 + 2*w_a*w_b*stdev_a*stdev_b*correl\n",
    "        stdev = sqrt(var)\n",
    "        X.append(stdev)\n",
    "        Y.append(r)\n",
    "    plot(X,Y,label='Correlation %0.0f%%' % (100*correl))\n",
    "xlabel('Standard Deviation $\\sigma$'), ylabel('Expected return $r$')\n",
    "title('Diversification benefit for different levels of correlation between two assets')\n",
    "legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
